This Application claims priority to pending German patent application 19949107.0 entitled HIGHLY TIME RESOLVED IMPEDANCE SPECTROSCOPY filed Oct. 12, 1999, and pending German patent Application 10018745.5 entitled HIGHLY TIME RESOLVED IMPEDANCE SPECTROSCOPY filed Apr. 15, 2000 both of which are incorporated by reference in their entirety herein.
1. Field of the Invention
This invention relates generally to the measurement of electrical impedance and, more particularly, to electrochemical impedance spectroscopy.
2. Description of Related Art
Impedance spectroscopy is a procedure used to characterize the electrical and electrochemical properties of investigated systems, and their changes over time. Typically, an a.c. voltage signal is applied between a working electrode and a counter electrode. If applicable, a simultaneously applied d.c. bias voltage is monitored with a reference electrode. Both the applied a.c. voltage signal, as well as the current response of the system, are measured. The complex electrical resistance (termed the impedance Z(xcfx89)) of a system can be calculated as a function of the frequency from the quotients of the voltage and current signals in the frequency domain according to equation (1). The impedance values for a number of frequencies define the impedance spectrum.                               Z          ⁢                      xe2x80x83                    ⁢                      (            ω            )                          =                                                            U                ^                            ⁢                              xe2x80x83                            ⁢                              (                ω                )                                                                    I                ^                            ⁢                              xe2x80x83                            ⁢                              (                ω                )                                              .                                    (        1        )            
Various electrical properties of the system or electrochemical processes can be derived from the characteristics of the impedance spectra. Particularly for systems in which direct current cannot flow, a.c. or transient voltage signals must be used for investigations. Due to the high information content of impedance spectroscopy, it is frequently the preferred technique for measurement of impedance spectra. For example, in electrochemistry, impedance spectroscopy is a standard analysis technique for investigating e.g. corrosion processes, redox reactions, liquid and solid electrolytes, thin polymer films, membranes and batteries. Several papers have provided an introduction and overview of the technique and application of electrochemical impedance spectroscopy. See J. R. MacDonald: xe2x80x9cImpedance Spectroscopy.xe2x80x9d (John Wiley and Sons, New York: 1987) and C. Gabrielli: Technical Report No. No. 004/83. 1983; C. Gabrielli: Technical Report No. part. No. 12860013. 1990.), both of which are incorporated by reference in their entirety herein.
Impedance spectroscopy is also used to characterize semiconductor materials See A. Bard: Electrochemical Methods. (Wiley and Sons, New York: 1980); and in biotechnology (See B. A. Cornell, Braach-Maksvytis, L. G. King et al.: xe2x80x9cA Biosensor that Uses Ion-Channel Switches.xe2x80x9d Nature. 387, p.580-583 (1997). S. Gritsch, P. Nollert, F. Jxc3xa4hnig et al.: xe2x80x9cImpedance Spectroscopy of Porin and Gramicidin Pores Reconstituted into Supported Lipid Bilayers on Indium-Tin-Oxide Electrodes.xe2x80x9d Langmuir. 14 (11), 3118-3125 (1998). C. Steinem, A. Janshoff and M. Siber: xe2x80x9cImpedance Analysis of Ion Transport Through Gramicidin Channels Incorporated by reference in Solid Supported Lipid Bilayers.xe2x80x9d Bioelectrochemistry and Bioenergetics. 42 (2), 213 (1997). All of the above referenced publications are incorporated by reference in their entirety herein.
The use of impedance spectroscopy has increased greatly, particularly in the field of biotechnology. In most cases, the electrodes are modified by chemical or physical coupling of biofunctional molecules and aggregates (e.g. lipid/protein membranes). Impedance spectroscopy is also used to detect adsorption processes.
There are two forms of impedance spectroscopy: Measuring impedance spectra in the frequency domain, Method I; and in the time domain, Method II.
Method I (frequency domain procedure): In the first form, a sinusoidal signal at a constant frequency and amplitude is applied within a discrete period, and the complex impedance of this discrete frequency is determined. To obtain a spectrum, sequential signals at different frequencies are applied. The time resolution, defined as the length of time in which the determined spectra follow each other, is low in this form of impedance spectroscopy. The time for acquiring the data records that compose the spectrum is a multiple of the period of the lowest frequency contained in the spectrum. The precise duration also depends on the number of the frequencies in the spectrum. Following a frequency change, a transition period is allowed for the system to attain an equilibrium. The time resolution of a typical sequence of spectra is a few seconds to minutes depending on the observed frequency band.
Method II (time domain procedure): In the second form, a frequency rich a.c. voltage signal is applied such as square wave pulses, structured or white noise. By using Fourier transformation, the impedance spectrum can be determined from a single data record of the time course of the voltage and current signal. Therefore, the impedance spectrum is limited regarding the bandwidth and frequency resolution by the known limitations of Fourier transformation. The measurement time is normally at least as long as one period of the lowest frequency in the spectrum of interest. Usually a measuring period of several periods of the lowest frequency in the spectrum is required to sufficiently improve the signal to noise ratio. The maximum time resolution depends on the repetition rate at which the data records, or sets, for Fourier transformation are acquired. Because the impedance of all frequencies of the spectrum are measured simultaneously in this method, the time resolution is usually much better than that of the first method.
Method I is normally used to characterize stationary systems or systems exhibiting slow dynamics. Commercial devices (frequency response analyzers (FRA)), are available for these measurements. At present, method II is primarily used for measurements where the impedance spectra contain very low frequencies, for example, down to about 10xe2x88x924 Hz, as required in corrosion studies.
The electrical properties of non-stationary systems, which means systems whose properties are not constant over time, cannot be measured in many cases with a sufficient time resolution by either Method I or Method II procedures of impedance spectroscopy. The time averaging effect of method I (summing for several periods of all the frequencies in the spectrum) and method II (over several periods of the lowest frequency contained in the spectrum) does not allow changes in the system over time, which are faster than the averaging time, to be resolved by a sequence of impedance spectra. The averaging time must be greatly reduced for impedance spectrometers to measure non-stationary systems with sufficient time resolution. A single impedance spectrum would then indicate the electrical states of the system localized in time. In addition, the individual spectra must be determined with high repetition rate to determine the time course of the system-characterizing quantities with a maximum time resolution.
An example of a non-stationary system that have not been able to be measured with conventional impedance spectroscopy includes lipid bilayer membranes with integrated, switching ion channels. The kinetics of many biological processes such as opening and closing ion channels in lipid bilayer membranes occurs on a time scale of a few milliseconds. These systems are highly relevant in the fields of biotechnology and human physiology.
Another example of a non-stationary system that has not been able to be measured with conventional impedance spectroscopy is metal and semiconductor interfaces with liquid and solid electrolytes with highly dynamic interface processes. In characterizing semiconductors and in the field of electrochemistry, conventional impedance spectroscopy cannot be used for many dynamic processes such as the in situ observation of rapid etching processes or the relaxation of electrochemical systems after voltage jumps since the necessary time resolution is impossible in the required bandwidths.
From the discussion above, it should be apparent that there is a need for a impedance spectroscopy method and apparatus that can measure non-stationary systems with high dynamics. The present invention fulfills this need.
A method and apparatus to measure impedance and impedance spectra in rapid sequence. Measurement of impedance, and impedance spectra, in rapid sequence provides repeated or continuous characterization of the electrical properties of the system under investigation. Highly time resolved impedance spectroscopy enhances the measurement of the dynamics of non-stationary systems due to its enhanced time resolution.
Three aspects of highly time resolved impedance spectroscopy are: (1) an optimized, frequency rich a.c., or transient, voltage signal is used as the perturbation signal; (2) non-stationary time to frequency transformation algorithms are used when processing the measured time signals of the voltage U(t) and current I(t) to determine a sequence of impedance spectra, where each spectrum is localized in time; and (3) the system-characterizing quantities are determined from the impedance spectra using equivalent circuit fitting in a time-resolution-optimized form.